Space charge wave amplifiers



L. M. FIELD SPACE CHARGE WAVE AMPLIFIERS Sept. 11, 1956 Filed Dec. 29. 1951 37 hmmm" Mlilllmlmw 38 auTPu-rr lNVENTOR .L 5575/? M. F/EL f www l ATTORNEY United States Patent Oce 2,762,948 Patented Sept. 11, 1956 SPACE CHARGE WAVE LmERs Lester M. Field, Palo Alto, Calif., assigner to The Board of Trustees of the Leland Stanford Junior University, Stanford University, Calif., a legal entity of California having corporate powers Application December 29, 1951, Serial No. 264,031 7 claims. (icl. sus- 3.6)

This invention relates to improvements in the art of amplifying high frequency electromagnetic wave energy, and particularly to methods and apparatus for eifecting amplification by means of space charge waves on a stream of electrons.

One of the principal objects of the invention is to provide electron discharge tubes capable of a high degree :of yamplification throughout extremely Wide bands of microwave frequency spectrum.

Another object is to provide high frequency amplifier devices of rugged and simple construction, wherein modulation of an extended electron beam is built up by a succession of abrupt changes in D.C. velocity along the beam.

The invention will be described with reference to the accompanying drawings, wherein:

Fig. lis a schematic diagram of an amplifier embodying the invention in a presently preferred form,

Fig. 2 is a graph showing the D.C. potential distribution and D.C. velocity along the path of the electron stream in the tube of Fig. 1,

Fig. 3 is a graph showing the amplitude of the A.C. current and A.C. velocity in the electron stream as a function of position along the path, corresponding to the potential distribution of Fig. 2, and

Fig. 4 is a schematic diagram of a modified embodiment of the invention, incorporating two cascaded stages.

yThe present application is a continuation-in-part of U, S. patent application Serial No. 253,344, entitled Space Charge Wave Amplifiers and led October 26, 1951, in the 'names of Ping King Tien and Lester M. Field.

According to this invention, the signal to be amplified is impressed on an electron beam to set up plasma oscillations or space charge waves comprising correlated variations of A.C. current density and A.C. velocity along the beam. The beam is then decelerated abruptly, at a point where the A.C. velocity is at a maximum, to a relatively low D.C. or average velocity which may be a small fraction of its initial D.C. velocity. Then, at a subsequent point along the path of the beam when the A.C. velocity due to the impressed signal is Zero, the beam is abruptly accelerated to a relatively high D.C. velocity, for example that which it had where the signal was applied. This series of operations on the beam produces a newset of space charge Waves like those caused by the'input signal, but of substantially greater amplitude. The'process may be repeated a number of times on the same beam, if desired, bydecelerating the beam and accelerating it again at successive respective points yoffmax- -V imum and zero A.C. velocity. Each repetition produces a considerable increase in the modulation of the beam, up to the point where the A.C. velocity and A.C. current density become large enough to cause saturation effects. The amplified signal may be taken oi the beam by suitable means responsive to A.C. current density and/or A.C. velocity, for example a conductive helix.

The amplifier shown in Fig. 1 includes an electron gun 1 arranged to project a beam of electrons along a longitudinal axis to a collector electrode 3. The gun 1 may be of known design, comprising a cathode 5, focussing electrode 7, and an anode or accelerator electrode 9. A short conductive helix V11 surrounds the path of the electron beam in the region of the gun 1. A similar helix 27 surrounds the path of the beam near the collector 3. The initial turn of the helix 11 may be stretched out as shown at 15 to provide a small probe or antenna for coupling to an input wave guide 33. The helix 27 is similarly coupled at 29 to an output guide 35.

' The helices 11 and 27 are similar to those used in travelling wave tubes, but they need not be made long enough to produce any substantial amplication. Their purpose is to modulate the beam with an input signal, applied to the guide 33, and to take the amplified signal 01T the beam for transmission by the output guide 35 to utilization means. While Vit is preferred at` present vto use helices as shown, rother known means may be employed for modulating the beam and extracting oscillatory energy from the beam, for example electrodes such as grids. In a typical tube which has been constructed, the helices 11 and 13 were wound of 0.01 inch diameter tungsten wire with a pitch of 26 turns per inch, and an inside diameter of 0.1 inch.

A plurality of apertured conductive disc electrodes 17, 18, 22, 24 and 26 surround the path of the electron beam at spacedl points between the helices 11 and 27. The electrodes 17 and 18 may be connected together by a cylindrical conductive tube 13 as shown, for supporting them in alignment within the vacuum envelope 39. The firstelectrode 17 is disposed adjacent the inner end of ythe input helix 11, and may be connected thereto. The second electrode 18 is spaced from the rst by a distance indicated as D on the drawing. Thisv distance depends upon the conditions under which the tube is designed to operate, and may, in a typical case, be about one and three quarters inches.

The thirdelectrode 22 may be located as near the electrode 18jas is feasible without the risk of voltage breakdown and 'arcing between the two elements. The fourth electrode 24 is spaced from the electrode 22 by a'distance D', determined by the operating conditions, as will be explained. The separation between the electrodes 22 and 24 may in some cases be the same as that between electrodes 17 and 18. The electrodes 22 and 24 are connected togetherby a tubular member 19, like the tube 13. The fourth and fth electrodes 24 and 26 are separated by a relatively small space, like that between the electrodes 18 and 22. The electrode 26 may be connected internally to the end of the output helix 27.

A D.C. source 37 is connected as shown to maintain the accelerator'9, and helices 11 and 27, the electrodes 17, 18 and 26, and the collector 3 at a high positive potential with respect to the cathode 5. In a tube having the dimensions and proportions given above, this potential may be about 1900 volts. The electrodes 22 and 24 are connected to a point 38 of relatively low voltage, say about .velocity of the beam as it leaves the gun and passes through the helix 11 is relativelyV high, owing to the high potential of the accelerator 9. This velocity should be substantially equal to the velocity of wave propagation along the helix 11, e. g. about one tenth the velocity of light. The term D.C. velocity as used herein means the average velocity of the electrons in the part of the 3 stream under consideration, and is designated by the letter u.V Cyclical variations in the velocity of electrons passing through a given plane across the stream are referred to as the A.C. velocity.

In an ideal unmodulated electron stream, all of the electronsmove at the D.C. velocity u, and the electron density or charge density remains constant at a D.C. value p. Now consider the stream to be sinusoidally modulated by cyclically accelerating and decelerating it at some transverse plane. The velocity at this plane is then u-i-v sin 21rfmt, where v is the magnitude of the A.C. velocity and fm is the modulation frequency. Assume that` v is much less than u, as is the case in the practice of the present invention. As the stream ows on, the electrons which are accelerated will get ahead of their normal or equilibrium positions, and those which are decelerated will get behind their` equilibrium positions, so that the stream becomes formed into relatively concentrated bunches of electrons which are separated by rarited regions.

Owing to the mutual repulsion between electrons, the bunches will spread out and coalesce, and the stream will be of substantially uniform density again at some point along its path. Here the electrons are in their original equilibrium positions with respect to each other, the axial repulsion forces exerted on each electron by those ahead of it being balanced by those behind it. However, the electrons at this point are moving with respect to their equilibrium positions, and momentum carries them past those positions in the opposite directions from `those in which they were originally displaced. Thus the stream is hunched again, at some subsequent point, and the cycle repeats itself.

This phenomenon is called plasma oscillation, or space charge oscillation. The frequency fp of oscillation of the electrons about their equilibrium positions depends upon the restoring force exerted on an electron per unit of its longitudinal displacement from equilibrium, and is substantially proportional to the square root of the D.C. charge density p. The distance through which the stream moves at the D.C. velocity u during one cycle of such oscillation is A v)cp and is` called the space charge wavelength, Ap; A Where the bunching is complete, the electrons are reversing their directions of motion with respect to the stream as a whole, i. e. those which have been travelling more slowly, having nearly been overtaken by the bunch, are being repelled forward and accelerated, and those faster ones which have nearly overtaken the bunch are repelled in the rearward direction from the bunch. Thus, the A.C. velocity v at these points is zero, notwithstanding the fact that the stream is modulated. This statement is based on the assumption that the original velocity modulation is small compared to the D.C. velocity u, so that the electrons do not have enough momentum to overcome the repulsion forces and pass through the bunch. The distance along the stream between consecutive points of zero A.C. velocity is one half the space charge wavelength, and these points are fixed with respect to the point where the modulation is applied. Midway between these points, the A.C. velocity is maximum, alternately in the direction of the stream and in the opposite direction. Thus the magnitude of the A.C. velocity varies periodically as a function of distance along the beam from any fixed reference point, the length of the complete period being one space charge wavelength. This variation of the magnitude of the A.C. velocity with position along the path of the stream may be regarded as a standing wave, fixed in space.

Where the A.C. velocityiis at a maximum, either positive or negative, the electrons are in their equilibrium positions and therefore the current density is uniform at the D.C. value qD. At all other points in the beam the current density will vary at themodulation frequency fm, above and below q by some amount q. This is the A.C. current density, and it also varies in magnitude as a function of distance along the beam, being zero where the A.C. velocity is maximum, and maximum where the A.C. velocity is zero. Thus we have a standing wave of A.C. current density magnitude, correlated with the A.C. velocity magnitude wave, and degrees out of space phase with it. The amplitudes of these waves are definitely related to each other because all of the modulation energy is transferred cyclically from one form to the other.

The modulation may be applied as pure velocity varian tion, as described above, or as density variation, since either one will become converted to the other and back again, producing the same sort of space charge waves. Furthermore, a mixture of the two kinds of modulation will do the same thing, the effect being to start the waves at a point where neither is of zero amplitude.

In the device of Fig. l, an input signal applied through the wave guide 33 to the helix 11 will modulate the elec tron stream, in the same manner as in a travelling wave tube. When the beam leaves the helix, it carries correlated waves of A.C. velocity and A.C. current density due to space charge oscillation, the space charge frequency fp and wavelength xp being determined by the D.,C. charge density p and D.C. velocity u.

Referring to Fig; 3, it is assumed for generality that the space charge waves at the point a at the electrode 17 on the end of the helix 11 have a current density amplitude qa and velocity amplitude va, neither being zero. At some subsequent point b along the stream, the A.C. current density will be zero and the A.C. velocity will be at a maximum value vb. The distance D between electrodes 17 and 18 (Fig. l) is determined in accordance with the initial D.C. charge density p and velocity u, and the relationship between A.C. current density and velocity at the point a, so as to make the velocity maximum vb occur approximately at the plane of the electrode 18. This distance may be found experimentally, or computed analytically, taking into account that the plasma frequency and space charge wavelength differ from their ideal values because the stream is of nite cross section. As a practical matter'the distance D is not very critical, and may differ widely from the theoretical optimum Without serious effect upon the operation of the tube.

In crossing the gap 21 between the electrodes 18 and 22, the beam is decelerated abruptly from the relatively `high D.C. velocity u, corresponding to say 1900 volts,

to a relatively low D.C. velocity u corresponding to the potential of the electrode 22, for example 65 volts. The total D.C. beam current I is the same on both sides of the gap 21, and is the product of the D.C. velocity and D.C. charge density at each point. Therefore where p is the charge density on the low potential side of the gap 21. As mentioned above, the plasma frequency is proportional to the square root of the D.C. charge density. Accordingly, the plasma frequency in the space between the electrodes 22 and 24 is The space charge wavelength, being equal to the D.C. velocity divided by the plasma frequency, is proportional to the three halves power of the velocity:

Thus the original set of space charge waves is converted at the gap 21 to a new set, similar to the iirst but of substantially shorter wavelength, Np. f

Consider an electron having a D.C. velocity u1. The kinetic energy is 1/zmu12, where m is the electron mass. Let the electron be decelerated by passing through a potential drop of E volts. The kinetic energy is then less by the amount Ee, where e is the electron charge, and

u2 being the D.C. velocity after deceleration, Now suppose that besides the D.C. velocity u1, the electron had a relatively small A.C. velocity of instantaneous value v1. Then the kinetic energy before deceleration is (from the above equation) Collecting the terms and factoring m, this becomes uiv1|1/2v12=u2v2i1/2v22 Since v1 and v2 are small compared to u1 and v1, their squares can be neglected, and

The instantaneous A.C. velocity after deceleration is therefore It is apparent that the new A.C. velocity is greater than the initial A.C. velocity, in the same ratio that the original D.C. velocity is greater than the new D.C. velocity.

Returning to Fig. 3, the A.C. velocity vb on the exit side of the gap 21 is times that of the original waves. The A.C. current amplitude is correspondingly increased, reaching a maximum value qe at a point c, one quarter space charge wavelength further along the beam.

The distance D between the electrodes 22 and 24 is made equal to one quarter the new space charge wavelength tp, so that the gap 25v is at the point c, or it may be any odd integral multiple of This distance may be computed, like the distance D. Correction for a small error in the value of D may be made by adjustment of the voltage at electrodes 22 and 24 by means of the voltage divider 40, to change'the space charge wavelength Ap and make the current density maximum occur at the plane of the electrode 24.

' In crossing the gap 25 between electrodes 24 and 26, the beam is accelerated abruptly to a relatively high D.C. velocity which, in the present example, is the same as the original velocity zz. This starts a further set of space charge waves having the same wavelength Ap as the original set. Owing to continuity of current across the gap, the A.C. current density on both sides is qu. Since the A.C. velocity on the entrance side is zero, it is also zero on the exit side. Accordingly, the new waves start at the point c with A.C. current density maximum, A.C. velocity zero.

On leaving the gap between electrodes 24 and 26, the beam has the same D.C. velocity and D.C. charge density as it had when it left the helix 11, as well as the same kind of modulation. However, the A.C. current density is much greater than it would have lbeen if the beam had simply travelled at its original D.C. velocity, and the beam is carrying space charge waves like those originally started on it by the input signal, but of larger amplitude, corresponding to qmm=qal l After the last acceleration at c, the beam goes through the output helix 27, including a wave thereon which gets its energy from the beam modulation and travels to the element 29 and into the output guide 35. Finally the beam strikes the collector electrode 3.

The total gain provided Iby the amplifier depends upon the structural design and the ratio between D.C. velocities u and u. The helices 11 and 27 may also contribute some gain, or loss, depending upon their lengths. Although the device of Fig. l has only one stage comprising a single deceleration followed by re-acceleration, any number of such stages may be similarly cascaded along a single beam, each additional stage providing additional gain, up to the point where the modulation of the beam, with a given input signal, becomes so great that small signal conditions no longer obtain. The structure of Fig. l, when operated with 1900 volts on electrodes 17, 13 and 26, and 65 volts on electrodes 22 and 24, provides a gain of about 24 db at a frequency of 3000 megacycles per second, with a beam current of 0.6 milliampere.

The two stage amplier shown in Fig. 4 includes an electron gun 1, collector 3, and input and output helices 11 and 27, all substantially the same as the correspondingly designated elements in Fig. l. A series of apertured electrodes 41, 43, 45, 47, 49, 51, 53 and 55 are disposed between the inner ends of the helices 11 and 27 to define short axial gaps 42, 46, 50 and 54. The electrodes may be supported as shown by tubular members 58, 44, 48, S0 and S6 engaging the inner surface of the envelope 39. ln a model of the device of Fig. 4 which has been constructed, the distance D between the gaps 42 and 46 is 0.86 centimeter. The distance D between the gaps 46 and 50 is 5.10 cm. The distance D between gaps 50 and 54 is the same as D", 0.86 cm.

An external D.C. source 37 is connected as shown to maintain the accelerator 9, collector 3, helices 11 and 27 and electrodes 58 and 56 at a high positive potential, for example 680 volts, with respect to the cathode 5. The electrodes 43 and 45 are supplied' with a relatively low voltage, for example 66 volts. Electrodes 47 and 49 are held at a high potential, such as 500 volts. Electrodes 51 and 55 are at a low potential, for example 50 volts.

In the operation of the device, the electron beam is modulated by interaction with the input Wave on the helix 11, then abruptly decelerated at the gap 42, which is in this instance located approximately at a velocity maximum, like the gap 21 in Fig. 1. A current maximum occurs at the gap 46, and here the beam is abruptly accelerated. A quarter space charge wavelength further on, at the gap 50, there is another velocity maximum, and the beam is again decelerated abruptly. At the gap 54 there is another current maximum, and the beam is accelerated again here to its original velocity, corresponding to 680 volts in the present example.

The A.C. velocity is increased upon each deceleration, as described in connection with Fig. l, and the original D.C. velocity is partly or wholly restored to its original value upon each acceleration. When it leaves the gap S4 and enters the output helix, the beam is modulated in the same manner as it was when it left the input helix, but to a much greater extent. The amplied signal is the' waveA guides.

' shownjhere by way of. illustration. j i I z Since many changes could lbemade inltl'aeabovc :coul struction land many apparently' widely .different .cmbodiy ments 1ot this invention lcould be' made without departing; l tfrorjn the scope thereof', it Ais 'intended that all-y instituerl l :contained in the above'description ors'hownin the accom-- panying drawings shall be. interprct'edas illustrative; and

'notinalimitingsense.' V- ='-.'r-.': n

"-deiivefea by way ordenan 211m .ne @apagada as as in: theI system of Fig.l 1.'

- n With typical operating voltages :as given above,l the i 1 iquen'cy fof 2891 megacycles per second; with lay ybeam `cur-A l 9'db of'this gainis contributed by-j the. helices, acting' :as inya itravelling; wave amplier,` j

' f In the present stage of the art,'the bandwidth .of the lamplier limited principally by krthat of the' tertnnations, i. e.y the coupling:meansV betweenl thel helices and .It'wili be apparent that any knowny broa' band .terminations may: -be used `instead ofi those rent of 0.5. milliampere.

What isclaimedis:y

' .f j tially the lsan-ie finaximum .amplitudes as said second :set-

andr approximately the same vI).+C.ve locity assaclifrst set,A and means coupled to .said lbeam beyond. ysaid sub-. f

` sequentfpoint and responsive to Saidfurtherset of space i charge waves gto. produce .au amplitudeversionA of said .inputwave energy. y

' A4.. Ai space charge .wave amplifier .including means .adapted to; direct atocussed beam' ujfl electronsalong an axis, means for. modulating the beam with input signals gto be amplified: for providing correlattxll space charge Awaves Cit alternating velocity; and alternating current density on' said beam, a plurality `of electrodes at. spaced i v lpoints' along` said axis anddening .alternate decelerating ygaps and accelerating gaps, said gaps being v ery. short .relativeto theirspacings :from each other: softhat the elecf' trouscan'no't appreciablychange their; relative {spacings j j i during transitv otzthegaps, andseparatedfrem each .other by distances substantially equal toodd integral mutliplGS; 1 l .o t'one quzar'tertbe space -chargewavelengt-hs inthe spaces I betweenthe vrespeetiye; gaps, land-meansadjacentthe path g .of-said beam beyond said electrodesresponsiveto modulation of the beam after its passage through 'said'y .series. lof gaps ito v pro-duce an amplified version of said input signals.

.1. A; space charge. wave amplifier: including an elec tronv gun adznptedl to' direct a ffocussed'beam. of; electrons l f along a 'substantiallyy linear path, va' .conductivel helixcolaxially. surrounding. a :part of' :said path: adjacent said i electron gun, fand: means vfor supplyinglhigh-y frequency. l

electromagnetic wave; energy rwhich iste-be amplifiedto 'said helix lto modulate said' beam and produ'cef longitu`;

` ofi' apertured electrodes surroundingsaid pathand Idefin` ling a deccleratng gap ata 'point where the' alternating current? density' amplitude of said' fbeam is substafntialiy f aero, saidlgapbei'ng very short comparedto the wave-f l ilengthof. said oscillation; on' said beam,l .anotherpair of.

. 'aperltured electrodes; surrounding said.y path and; defining f i an accelerating' gap at a' subsequent lpoint on said path 1 where; thel alternating: velocity amplitude Vof" ysaid beam, f 1

' is substantially'zero, said* subsequent pointl being spacedf from said first mentioned point by a distance that is substantially an odd integral multiple of one quarter of the wavelength of the plasma oscillation on said beam in the space between said gaps, said second gap being Very short compared to said wavelength, a second conductive helix surrounding a part of said path beyond said electrodes, and means for taking amplified wave energy off said helix.

2. A space charge wave amplifier including an input helix and an output helix, said helices being coaxial and longitudinally spaced apart on their common axis, means for producing and directing a beam of electrons along said axis through said input and output helices in succession, means for applying an input signal to be amplied to said input helix to modulate said electron beam and produce space charge oscillations therein, and electrode means in the space between said helices defining a deceleration gap followed by an acceleration gap, said deceleration and acceleration gaps being very short compared to the distance between them.

3. A space charge wave amplifier including means for producing an electron beam, means responsive to high frequency electromagnetic wave energy input to modulate said beam and produce correlated space charge Waves of alternating velocity and alternating current density thereon, the amplitudes of said waves varying periodically with longitudinal position on the beam, means for abruptly decelerating said beam at a point on its path where the alternating current density is approximately zero, to convert said space charge waves to a second set of waves having higher maximum amplitudes associated with a lower D.C. velocity, means for abruptly accelerating said beam at a subsequent point on its path where the alternating velocity is substantially zero, to convert said second set of waves to a further set having substanf l 55.2 A2 space Chars@ wave amplifier;ncludinsmfbans'fof' g iproducingafmodulatedelectron beam carrying correlated waves olf .current 'density vand velocity variation. and a; y

fseries of apertured electrodes at; spaced points .alongthe f l f pathof the beam defining at Aleast one deceleration gap -foilowed .by ati least ionev 'acceleration gap; both -ot saidr i gaps :being short .relative to the space-:charge `Wavelengthr so that the. electronslcannot. -appreciably :change @their i relative .spacings during.' transit `of the gaps with the.

' decelerationl gap being in theyicinity of a'veiocity1 maxi*y l mum ofsaid waves and ,the acceleration gap being in they vicinity of a velocity minimum of =said waves. and sepa.-

rated: from each other by a distance substantially equal to one lquarter the lspace charge lwavelength onl the part. f

f of the. beam. betweensaid gaps. l

producing a beam of electrons and directing said beam along a substantially lineal path with an initial D. C. velocity u, and D. C. charge density p, means for modulating said beam with an input signal to produce correlated waves thereon of A. C. current density variation of amplitude q and A. C. velocity variation of amplitude v, said waves having a length Ap determined by said D. C. velocity u and D. C. charge density p; means for abruptly decelerating said beam to a lower D. C. velocity u', at a point where said A. C. current density q is substantially zero, to convert said waves to different waves having A. C. current density amplitude q and A. C. velocity amplitude v, with a length Ap which is shorter than Ap; means for abruptly accelerating said beam at a second point distant from said first point, to a higher D. C. velocity approximately the same as said initial D. C. velocity u, and means surrounding a portion of said path subsequent to said accelerating means and responsive to the modulation on said beam to reproduce said input signal.

7. A space charge wave amplifier, including means for producing a modulated electron beam carrying correlated waves of alternating charge density and alternating velocity having a predetermined space charge wavelength, first means located at a first region along said beam in the vicinity of a space charge wave alternating charge density minimum for decreasing the Wavelength and increasing the amplitudes of said space charge waves, and second means located at a second region along said beam in the vicinity of a space charge Wave alternating charge density maximum for decreasing the wavelength and increasing the amplitudes of said space charge waves, each of said first and second means being adapted to modify predetermined characteristics of said beam along a region substantially shorter than one-quarter of the space charge wavelength.

References Cited in the le of this patent UNITED STATES PATENTS 2,190,511 Cage Feb. 13, 1940 10 Metcalf Feb. 27, 1940 Hahn Nov. 26, 1940 Posthumus et a1. May 2, 1944 Llewellyn Jan. 16, 1,945 Hansen et al. Aug. 27, 1946 Coeterier Ian. 16, 1951 Tiley Feb. 13, 1951 

